(1 point) Suppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is µa = 0. 86 57 59 62 88 86 90 y 84 81 63 60 94 62 74 Use a 0.05 significance level to find the following: (a) The mean value of the differnces d for the paired sample data d = (b) The standard deviation of the differences d for the paired sample data SA = (c) The t test statistic t = (d) The positive critical value t = (e) The negative critical value t =

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Problem Description:**

Suppose you want to test the claim that the paired sample data given below come from a population for which the mean difference is \( \mu_d = 0 \).

|        | x  | y  |
|--------|----|----|
| Data   | 86 | 84 |
|        | 57 | 81 |
|        | 59 | 63 |
|        | 62 | 60 |
|        | 88 | 94 |
|        | 86 | 62 |
|        | 90 | 74 |

**Instructions:**

Use a 0.05 significance level to find the following:

(a) The mean value of the differences \( \bar{d} \) for the paired sample data.
\[ \bar{d} = \text{[Input Answer]} \]

(b) The standard deviation of the differences \( s_d \) for the paired sample data.
\[ s_d = \text{[Input Answer]} \]

(c) The t test statistic.
\[ t = \text{[Input Answer]} \]

(d) The positive critical value.
\[ t = \text{[Input Answer]} \]

(e) The negative critical value.
\[ t = \text{[Input Answer]} \]

(f) Does the test statistic fall in the critical region?

- A. Yes
- B. No

(g) Construct a 95% confidence interval for the population mean of all differences \( x - y \).
\[ \text{Lower Limit} < \mu_d < \text{Upper Limit} \]
Transcribed Image Text:**Problem Description:** Suppose you want to test the claim that the paired sample data given below come from a population for which the mean difference is \( \mu_d = 0 \). | | x | y | |--------|----|----| | Data | 86 | 84 | | | 57 | 81 | | | 59 | 63 | | | 62 | 60 | | | 88 | 94 | | | 86 | 62 | | | 90 | 74 | **Instructions:** Use a 0.05 significance level to find the following: (a) The mean value of the differences \( \bar{d} \) for the paired sample data. \[ \bar{d} = \text{[Input Answer]} \] (b) The standard deviation of the differences \( s_d \) for the paired sample data. \[ s_d = \text{[Input Answer]} \] (c) The t test statistic. \[ t = \text{[Input Answer]} \] (d) The positive critical value. \[ t = \text{[Input Answer]} \] (e) The negative critical value. \[ t = \text{[Input Answer]} \] (f) Does the test statistic fall in the critical region? - A. Yes - B. No (g) Construct a 95% confidence interval for the population mean of all differences \( x - y \). \[ \text{Lower Limit} < \mu_d < \text{Upper Limit} \]
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